Accelerated Alternating Descent Methods for Dykstra-like ProblemsMS59

We present an alternating descent scheme for problems involving nonsmooth objectives with a quadratic term. Our algorithm performs in each variable several descent steps, which improves the performances over a single step. Thanks to a FISTA-like trick, this scheme can also be accelerated. Linear convergence rates are established under strongly convexity. An application of this work is the implementation of a fast parallel solver for the proximity operator of the Total Variation for color images.

This presentation is part of Minisymposium “MS59 - Approaches for fast optimisation in imaging and inverse problems (3 parts)
organized by: Jingwei Liang (University of Cambridge) , Carola-Bibiane Schönlieb (University of Cambridge) , Mila Nikolova (CMLA - CNRS ENS Cachan, University Paris-Saclay) .

Pauline Tan (CMLA, École normale supérieure Paris-Saclay)